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Quadrilateral is an important topic in mathematics. The students who are preparing for SAT/ACT need to study Quadrilaterals as they are going to use the concept of Area and perimeter of quadrilaterals at college courses later.

Basically a Quadrilateral is a closed figure with four sides and angle; the sum of the interior angles of a quadrilateral is 360⁰. Based on the length of sides and angles between adjacent sides, quadrilaterals are classified as follows.

Rectangle

A Rectangle is a closed figure whose opposite sides are parallel and equal and the angle formed between two adjacent sides is always 90⁰. Let’s say ‘a’ is the length of the rectangle and ‘b’ is the width. Area and perimeter of rectangle is given by

Area= a * b Square Units

Perimeter = 2(a+b) Units

Figure 1: Rectangle

Square

A Quadrilateral is a square in which all sides are equal and parallel and the angle between adjacent sides is 90⁰. The Figure below is an example of a square in which AB ∥ DC, AD ∥ BC, AB = BC = CD = DA and ∠A = ∠B = ∠ C = ∠D = 90°. Diagonals are equal and are perpendicular bisectors of each other. Every square is a parallelogram, rectangle and a rhombus in which diagonals are congruent and bisect the angles

Let ‘a’ is the length of sides of a square, Area and perimeter is given by

Area= a² square units

Perimeter = 4a Units

Figure 2: Square

Parallelogram

Parallelogram is a quadrilateral in which two pairs of opposite sides are parallel and congruent in length. Opposite angles of a Parallelogram are equal, diagonals divide the parallelogram into two congruent triangles.

An example of a parallelogram, with congruent parts identified, is shown below.

Area and perimeter of a parallelogram is

Area = Base x Height     square units

Perimeter= AB+ BC+CD+DA     units

Figure 3: Parallelogram

Rhombus

Parallelogram with four sides of equal length is called a Rhombus. Diagonals of a Rhombus are perpendicular bisectors of each other and each diagonal is the angle bisector of both the opposite angles.

Area = Base x Height    square units

Perimeter= AB+ BC+CD+DA     units

Area of Rhombus in terms of diagonal is

Area = (d₁* d₂)/2

Figure 4: Rhombus

Trapezoid

A quadrilateral with one pair of parallel opposite sides is called a trapezoid. Diagonals of a trapezoid intersect in the same ratio and adjacent angles are supplementary angles.

Figure 5: Trapezoid

Kite

A kite is a Quadrilateral in which the adjacent sides are equal. The diagonals of a kite are perpendicular to one another. This results in the diagonals creating right angles at the points of intersection. The Figure below shows an example of kite in which adjacent sides KL=LM and JK=JM. The angles that are opposite to each other and between two different lengths are congruent (∠K=∠M) and the longer diagonal bisects angle Land J.

Area= (JL*KM)/2   Square units

Perimeter=JK+KL+LM+MJ   Units

Figure 6: Kite

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